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The OZ equation has practical importance as a foundation for approximations for computing the pair correlation function of molecules or ions in liquids, or of colloidal particles. The pair correlation function is related via Fourier transform to the static structure factor , which can be determined experimentally using X-ray diffraction or ...
Simplified formula for the Ornstein–Uhlenbeck process from the mural shown below. Dutch artist collective De Strakke Hand: Leonard Ornstein mural, showing Ornstein as a cofounder of the Dutch Physical Society (Netherlands Physical Society) at his desk in 1921, and illustrating twice the random walk of a drunkard with a simplified formula for the Ornstein–Uhlenbeck process.
This is a list of scientific equations named after people (eponymous equations). [1 Equation Field Person(s) named after ... Ornstein–Zernike equation: Statistical ...
In statistical mechanics the hypernetted-chain equation is a closure relation to solve the Ornstein–Zernike equation which relates the direct correlation function to the total correlation function. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function .
In statistical mechanics the Percus–Yevick approximation [1] is a closure relation to solve the Ornstein–Zernike equation. It is also referred to as the Percus–Yevick equation. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. The approximation is named after Jerome K. Percus and George J ...
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems.
In 1914, Zernike and Leonard Ornstein were jointly responsible for the derivation of the Ornstein–Zernike equation in critical-point theory. In 1915, he became lector in theoretical mechanics and mathematical physics at the same university and in 1920 he was promoted to professor of mathematical physics. [4]
Using the Fourier representation of the Ornstein-Zernike equation the compressibility equation can be rewritten in the form: ...